Optimum pressure ratios of a regenerative gas turbine (RGT) power plant with and without a solid oxide fuel cell are investigated. It is shown that assuming a constant specific heat ratio throughout the RGT plant, explicit expressions can be derived for the optimum pressure ratios leading to maximum thermal efficiency and maximum net work output. It would be analytically complicated to apply the same method for the hybrid system due to the dependence of electrochemical parameters such as cell voltage on thermodynamic parameters like pressure and temperature. So, the thermodynamic optimization of this system is numerically studied using models of RGT plant and solid oxide fuel cell. Irreversibilities in terms of component efficiencies and total pressure drop within each configuration are taken into account. The main results for the RGT plant include maximization of the work output at the expenses of 2–4% lower thermal efficiency and higher capital costs of turbo-compressor compared to a design based on maximum thermal efficiency. On the other hand, the hybrid system is studied for a turbine inlet temperature (TIT) of 1 250–1 450 K and 10–20% total pressure drop in the system. The maximum thermal efficiency is found to be at a pressure ratio of 3–4, which is consistent with past studies. A higher TIT leads to a higher pressure ratio; however, no significant effect of pressure drop on the optimum pressure ratio is observed. The maximum work output of the hybrid system may take place at a pressure ratio at which the compressor outlet temperature is equal to the turbine downstream temperature. The work output increases with increasing the pressure ratio up to a point after which it starts to vary slightly. The pressure ratio at this point is suggested to be the optimal because the work output is very close to its maximum and the thermal efficiency is as high as a littler less than 60%.